{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:PCTR3OP4VIJELGJZDKDCAI3X6K","short_pith_number":"pith:PCTR3OP4","schema_version":"1.0","canonical_sha256":"78a71db9fcaa124599391a86202377f297350e714320a189b502512acf61b40c","source":{"kind":"arxiv","id":"1610.04874","version":2},"attestation_state":"computed","paper":{"title":"Coloring Graphs to Produce Properly Colored Walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Robert Melville, Wayne Goddard","submitted_at":"2016-10-16T15:48:32Z","abstract_excerpt":"For a connected graph, we define the proper-walk connection number as the minimum number of colors needed to color the edges of a graph so that there is a walk between every pair of vertices without two consecutive edges having the same color. We show that the proper-walk connection number is at most three for all cyclic graphs, and at most two for bridgeless graphs. We also characterize the bipartite graphs that have proper-walk connection number equal to two, and show that this characterization also holds for the analogous problem where one is restricted to properly colored paths."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1610.04874","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-16T15:48:32Z","cross_cats_sorted":[],"title_canon_sha256":"0608f8c519c09565d81f32408d9ba5d400f62af491634283107fd1c98f3b1b30","abstract_canon_sha256":"1f40be69a16a1486f179d81db1a251f68174aa155282b835e9abaf2cfb918752"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:58.569239Z","signature_b64":"2esRmleQcpApLhS4ob6IBQDWgnrdQ19oE10c60dS7qUjvUQ8HRAlU5VBnQKJqrii2NSaPBGeZi7wbN20PVgYDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78a71db9fcaa124599391a86202377f297350e714320a189b502512acf61b40c","last_reissued_at":"2026-05-18T00:45:58.568784Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:58.568784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coloring Graphs to Produce Properly Colored Walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Robert Melville, Wayne Goddard","submitted_at":"2016-10-16T15:48:32Z","abstract_excerpt":"For a connected graph, we define the proper-walk connection number as the minimum number of colors needed to color the edges of a graph so that there is a walk between every pair of vertices without two consecutive edges having the same color. We show that the proper-walk connection number is at most three for all cyclic graphs, and at most two for bridgeless graphs. We also characterize the bipartite graphs that have proper-walk connection number equal to two, and show that this characterization also holds for the analogous problem where one is restricted to properly colored paths."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04874","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1610.04874","created_at":"2026-05-18T00:45:58.568852+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.04874v2","created_at":"2026-05-18T00:45:58.568852+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04874","created_at":"2026-05-18T00:45:58.568852+00:00"},{"alias_kind":"pith_short_12","alias_value":"PCTR3OP4VIJE","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"PCTR3OP4VIJELGJZ","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"PCTR3OP4","created_at":"2026-05-18T12:30:39.010887+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PCTR3OP4VIJELGJZDKDCAI3X6K","json":"https://pith.science/pith/PCTR3OP4VIJELGJZDKDCAI3X6K.json","graph_json":"https://pith.science/api/pith-number/PCTR3OP4VIJELGJZDKDCAI3X6K/graph.json","events_json":"https://pith.science/api/pith-number/PCTR3OP4VIJELGJZDKDCAI3X6K/events.json","paper":"https://pith.science/paper/PCTR3OP4"},"agent_actions":{"view_html":"https://pith.science/pith/PCTR3OP4VIJELGJZDKDCAI3X6K","download_json":"https://pith.science/pith/PCTR3OP4VIJELGJZDKDCAI3X6K.json","view_paper":"https://pith.science/paper/PCTR3OP4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.04874&json=true","fetch_graph":"https://pith.science/api/pith-number/PCTR3OP4VIJELGJZDKDCAI3X6K/graph.json","fetch_events":"https://pith.science/api/pith-number/PCTR3OP4VIJELGJZDKDCAI3X6K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PCTR3OP4VIJELGJZDKDCAI3X6K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PCTR3OP4VIJELGJZDKDCAI3X6K/action/storage_attestation","attest_author":"https://pith.science/pith/PCTR3OP4VIJELGJZDKDCAI3X6K/action/author_attestation","sign_citation":"https://pith.science/pith/PCTR3OP4VIJELGJZDKDCAI3X6K/action/citation_signature","submit_replication":"https://pith.science/pith/PCTR3OP4VIJELGJZDKDCAI3X6K/action/replication_record"}},"created_at":"2026-05-18T00:45:58.568852+00:00","updated_at":"2026-05-18T00:45:58.568852+00:00"}